Abstract: In order to study the influence of nonlinear factors on the elastodynamics of spur gear’s pure torsional model, a pure torsional dynamic model of four-degree-of-freedom spur gear is established by using the principle of D’Alembert and the method of micro-displacement. Firstly, a time-varying equation set is solved by Runge-Kutta and time-dispersion methods with the consideration of the nonlinear factors such as gear meshing error, time-varying meshing stiffness and meshing gap, and the dynamic response and the corresponding spectrum of the system are obtained. Next, combined with the nonlinear analysis theory, the global bifurcation diagram and the maximum Lyapunov exponent are obtained by changing the meshing stiffness, the excitation frequency and the tooth side clearance of the system. Then, the periodic motion, quasi-periodic motion and chaos of the system are analyzed from the quantitative and qualitative point of view respectively by using the time history plot, phase space trajectory, Poincáre map and power spectrum. Finally, the coupling influence of nonlinear factors on the system are considered, which provides a complete method for the nonlinear characteristic analysis of gear transmission system.

Key words: spur gear, pure torsional dynamic model, bifurcation, maximum Lyapunov exponent, Poincáre map